Explain to them why you are doing what you are doing, what results you have achieved and show the potential of social media to deliver a real financial return. It will help consolidate your position in the company, ensure you get more freedom and responsibility, and may even win the social media team a greater allocation of company resources. If you are already the owner of a social media budget, sending a monthly report will help you justify the investment the company is making, and hopefully ensure the continuation and expansion of that commitment.
The same applies if you are an agency or a consultant working with clients. You do want to communicate your activities and results achieved, and a monthly report is the perfect tool for this.